{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eq(y(x), sqrt(2)*tan(sqrt(2)*x)/2)\n",
      "Eq(y(x), 2*exp(x) + (-1/2 + sqrt(5)/10)*exp(x*(1 - sqrt(5))/2) + (-1/2 - sqrt(5)/10)*exp(x*(1 + sqrt(5))/2))\n"
     ]
    }
   ],
   "source": [
    "#8.1\n",
    "\n",
    "#（1）\n",
    "import numpy as np\n",
    "import sympy as sym\n",
    "x = sym.symbols('x')\n",
    "y1 = sym.Function('y')\n",
    "eq1 = sym.diff(y1(x),x)-2*y1(x)**2-1#定义方程\n",
    "con = {y1(0):0}#定义初值条件\n",
    "y1 = sym.dsolve(eq1,ics = con)\n",
    "print(sym.sympify(y1))\n",
    "#(2)\n",
    "y2 = sym.Function('y')\n",
    "eq2 = sym.diff(y2(x),x,3)-2*sym.diff(y2(x),x,2)+y2(x)\n",
    "con2 = {y2(0):1,sym.diff(y2(x),x).subs(x,0):1,sym.diff(y2(x),x,2).subs(x,0):0}\n",
    "y2 = sym.dsolve(eq2,ics = con2)\n",
    "print(sym.sympify(y2))#求出来的解比较复杂"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eq(x(t), -sqrt(7)*exp(3*t/2)*sin(sqrt(7)*t/2)/7 + exp(3*t/2)*cos(sqrt(7)*t/2)) \n",
      " Eq(y(t), 2*sqrt(7)*exp(3*t/2)*sin(sqrt(7)*t/2)/7)\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#8.2\n",
    "\n",
    "import sympy as sym\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "t = sym.symbols('t')\n",
    "x,y = sym.symbols('x,y',cls = sym.Function)\n",
    "eq = [x(t).diff(t)-x(t)+2*y(t),y(t).diff(t)-x(t)-2*y(t)]\n",
    "con = {x(0):1,y(0):0}\n",
    "s = sym.dsolve(eq,ics=con)\n",
    "print(s[0],'\\n',s[1])\n",
    "u = np.linspace(0,1,100)\n",
    "xf = -np.sqrt(7)*np.exp(3.*u/2.)*np.sin(np.sqrt(7)*u/2.)/7. + np.exp(3.*u/2.)*np.cos(np.sqrt(7.)*u/2.)\n",
    "yf = 2.*np.sqrt(7)*np.exp(3.*u/2.)*np.sin(np.sqrt(7)*u/2.)/7.\n",
    "plt.plot(u,xf,'r')\n",
    "plt.plot(u,yf,'g')\n",
    "plt.show()#两个都是单调函数"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\goodboy\\AppData\\Local\\Programs\\Python\\Python39\\lib\\site-packages\\IPython\\core\\pylabtools.py:151: UserWarning: Glyph 8722 (\\N{MINUS SIGN}) missing from current font.\n",
      "  fig.canvas.print_figure(bytes_io, **kw)\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#8.3\n",
    "\n",
    "from scipy.integrate import solve_ivp\n",
    "def natural_convection(eta, y): # 将含有两个未知函数的高阶微分方程降阶，得到由2+3个一阶微分方程组成的方程组\n",
    "  T1 = y[0] #T函数的0阶导，即T函数本身\n",
    "  T2 = y[1]#T函数的1阶导\n",
    "  f1 = y[2]#f函数的0阶导，即f函数本身\n",
    "  f2 = y[3]#f函数的1阶导\n",
    "  f3 = y[4]#f函数的2阶导\n",
    "  return T2, -2.1*f1*T2, f2, f3, -3*f1*f3 + 2*(f2**2)-T1#其实最终还是化为最高阶导数的函数\n",
    "  #返回的依次为1阶导，2高阶导。。。高阶导\n",
    "eta = np.linspace(0, 10, 1000)#变量取值\n",
    "eta_span = [0, 10]#取值范围\n",
    "init = np.array([ 1, -0.5, 0, 0, 0.68])#题目给的初值条件\n",
    "curve = solve_ivp(natural_convection, eta_span, init, t_eval=eta)\n",
    "t = curve.t\n",
    "data = curve.y\n",
    "plt.rc('font',size =14)\n",
    "plt.rc('font',family = 'SimHei')\n",
    "plt.plot(t,data[0,:],label = 'T解曲线')\n",
    "plt.plot(t,data[1,:],label = 'f解曲线')\n",
    "plt.legend(loc ='best')\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 286,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  message: 'The solver successfully reached the end of the integration interval.'\n",
      "     nfev: 1478\n",
      "     njev: 0\n",
      "      nlu: 0\n",
      "      sol: None\n",
      "   status: 0\n",
      "  success: True\n",
      "        t: array([  0.        ,   1.01010101,   2.02020202,   3.03030303,\n",
      "         4.04040404,   5.05050505,   6.06060606,   7.07070707,\n",
      "         8.08080808,   9.09090909,  10.1010101 ,  11.11111111,\n",
      "        12.12121212,  13.13131313,  14.14141414,  15.15151515,\n",
      "        16.16161616,  17.17171717,  18.18181818,  19.19191919,\n",
      "        20.2020202 ,  21.21212121,  22.22222222,  23.23232323,\n",
      "        24.24242424,  25.25252525,  26.26262626,  27.27272727,\n",
      "        28.28282828,  29.29292929,  30.3030303 ,  31.31313131,\n",
      "        32.32323232,  33.33333333,  34.34343434,  35.35353535,\n",
      "        36.36363636,  37.37373737,  38.38383838,  39.39393939,\n",
      "        40.4040404 ,  41.41414141,  42.42424242,  43.43434343,\n",
      "        44.44444444,  45.45454545,  46.46464646,  47.47474747,\n",
      "        48.48484848,  49.49494949,  50.50505051,  51.51515152,\n",
      "        52.52525253,  53.53535354,  54.54545455,  55.55555556,\n",
      "        56.56565657,  57.57575758,  58.58585859,  59.5959596 ,\n",
      "        60.60606061,  61.61616162,  62.62626263,  63.63636364,\n",
      "        64.64646465,  65.65656566,  66.66666667,  67.67676768,\n",
      "        68.68686869,  69.6969697 ,  70.70707071,  71.71717172,\n",
      "        72.72727273,  73.73737374,  74.74747475,  75.75757576,\n",
      "        76.76767677,  77.77777778,  78.78787879,  79.7979798 ,\n",
      "        80.80808081,  81.81818182,  82.82828283,  83.83838384,\n",
      "        84.84848485,  85.85858586,  86.86868687,  87.87878788,\n",
      "        88.88888889,  89.8989899 ,  90.90909091,  91.91919192,\n",
      "        92.92929293,  93.93939394,  94.94949495,  95.95959596,\n",
      "        96.96969697,  97.97979798,  98.98989899, 100.        ])\n",
      " t_events: None\n",
      "        y: array([[100.        ,  94.23196124,  77.07160609,  55.61808743,\n",
      "         38.61572019,  28.56657241,  23.44473543,  21.02380277,\n",
      "         20.34618125,  20.88016953,  22.4480592 ,  24.91613288,\n",
      "         28.26551264,  32.5457356 ,  37.84969049,  44.27388084,\n",
      "         51.91474092,  60.80292577,  70.91843609,  81.71855636,\n",
      "         92.0168161 ,  99.14250999,  98.46799215,  86.09542173,\n",
      "         65.39457077,  45.83702774,  32.73505764,  25.44041636,\n",
      "         21.77733674,  20.36988857,  20.42317657,  21.54971309,\n",
      "         23.59648004,  26.54750251,  30.39935665,  35.21831746,\n",
      "         41.11661308,  48.18929371,  56.51265448,  66.0474072 ,\n",
      "         76.67821619,  87.4741085 ,  96.50099337, 100.17825212,\n",
      "         93.52599305,  75.70997073,  54.06964054,  37.28746292,\n",
      "         27.68408338,  22.74216024,  20.52357284,  19.95761846,\n",
      "         20.60242175,  22.24502049,  24.77622535,  28.17949321,\n",
      "         32.52016573,  37.89168578,  44.39823923,  52.13295006,\n",
      "         61.18013299,  71.4491074 ,  82.42889027,  93.48614868,\n",
      "        100.63299905,  99.12631471,  86.39372202,  64.83671989,\n",
      "         44.97980094,  31.98444096,  24.85902713,  21.36582456,\n",
      "         20.01313752,  20.02044747,  21.16556642,  23.22850049,\n",
      "         26.15821615,  29.98304229,  34.7885184 ,  40.67358485,\n",
      "         47.74315109,  56.08992291,  65.75599187,  76.46666418,\n",
      "         87.7985886 ,  97.62392191, 101.38854695,  95.3580274 ,\n",
      "         77.546654  ,  55.39704112,  38.32024796,  28.15949403,\n",
      "         22.87712756,  20.46170024,  19.77604582,  20.36241227,\n",
      "         21.93492907,  24.38457954,  27.7003559 ,  31.95668681],\n",
      "       [ 40.        ,  65.03774447,  93.92657987, 111.14437519,\n",
      "        107.78629777,  90.76999352,  70.70275991,  53.30679595,\n",
      "         39.63681233,  29.52504047,  22.16293226,  16.96461564,\n",
      "         13.37672182,  10.9758609 ,   9.4415832 ,   8.59873429,\n",
      "          8.41851118,   9.0046546 ,  10.52635953,  13.70284128,\n",
      "         19.88708007,  31.70764534,  52.48980917,  81.35632547,\n",
      "        105.65285536, 111.33335626,  99.4400759 ,  80.17571031,\n",
      "         61.31343637,  45.71869469,  33.86301013,  25.25009816,\n",
      "         19.13074481,  14.8220607 ,  11.89292474,   9.99375475,\n",
      "          8.85947015,   8.37856008,   8.57393457,   9.65767691,\n",
      "         11.93143801,  16.46481593,  25.26439288,  41.44999308,\n",
      "         67.22612914,  95.865652  , 112.09122478, 107.53513777,\n",
      "         89.6035276 ,  69.46584306,  52.05824981,  38.57412425,\n",
      "         28.60607856,  21.41725687,  16.36297281,  12.8971275 ,\n",
      "         10.57539549,   9.08630237,   8.27500689,   8.13801149,\n",
      "          8.69780825,  10.21333556,  13.41161682,  18.96473319,\n",
      "         31.39870324,  53.80055899,  83.19007586, 108.06769224,\n",
      "        113.00526097,  99.99811421,  80.02382769,  60.83719793,\n",
      "         45.21193428,  33.50667715,  24.88009665,  18.76422136,\n",
      "         14.51753433,  11.63657848,   9.72590262,   8.55390669,\n",
      "          8.05429968,   8.21872596,   9.14278709,  11.30235122,\n",
      "         15.23334973,  23.50107264,  40.41202463,  66.28598529,\n",
      "         96.2130274 , 113.47672534, 109.2639015 ,  91.73356638,\n",
      "         71.36020939,  53.49912938,  39.59630684,  29.24886355,\n",
      "         21.82813156,  16.62893849,  13.06405684,  10.63806455]])\n",
      " y_events: None\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[50. 40.]\n",
      "100个周期内兔子的最大值为：101.38854694863763,最小值为：19.776045816978574\n",
      "100个周期内狐狸的最大值为：113.47672533950826,最小值为：8.054299676628421\n",
      "兔子数量第一次达到最大值为的时间为：22,第一次达到最小值的时间为：8\n",
      "狐狸数量第一次达到最大值为：4,第一次达到最小值时间为：16\n"
     ]
    },
    {
     "data": {
      "text/plain": "'\\n兔子与狐狸之间动态平衡\\n可以尝试时间轴放大，以及放大初始种群数量,来看整体的变化情况\\n'"
     },
     "execution_count": 286,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#8.4\n",
    "\n",
    "#出现一个疑问，先求解符号解还是数值解？\n",
    "#先尝试解出x(t)和y(t)的符号解\n",
    "'''\n",
    "import sympy as sym\n",
    "t = sym.symbols('t')\n",
    "x1,x2 = sym.symbols('x,y',cls = sym.Function)\n",
    "eq = [x1(t).diff(t)-0.2*x1(t)+0.005*x1(t)*x2(t),\n",
    "      x2(t).diff(t)+0.5*x2(t)-0.01*x1(t)*x2(t)]\n",
    "con = {x1(0):70,x2(0):40}\n",
    "s = sym.dsolve(eq,ics = con)\n",
    "print(s)\n",
    "经过测试，sympy好像并不能解决这个问题（经过调试应该可以，但是我无法解决）\n",
    "'''\n",
    "from scipy.integrate import solve_ivp\n",
    "from scipy.optimize import fsolve\n",
    "import numpy as np\n",
    "def natural_convection(eta, y): # 将含有两个未知函数的高阶微分方程降阶，得到由2+3个一阶微分方程组成的方程组\n",
    "  x1 = y[0] #x函数的0阶导，即x函数本身\n",
    "  y1 = y[1]#y函数的0阶导，即y函数本身\n",
    "  return 0.2*x1-0.005*x1*y1,-0.5*y1+0.01*x1*y1\n",
    "  #返回的依次为1阶导，2高阶导。。。高阶导\n",
    "t = np.linspace(0, 100,100)#变量取值\n",
    "t_span = [0,500]#取值范围\n",
    "init = np.array([100,40])#题目给的初值条件\n",
    "curve = solve_ivp(natural_convection,t_span= t_span,y0= init, t_eval=t)\n",
    "print(curve)\n",
    "t = curve.t\n",
    "data = curve.y\n",
    "plt.rc('font',size =14)\n",
    "plt.rc('font',family = 'SimHei')\n",
    "plt.plot(t,data[0,:],label = '兔子数量曲线')\n",
    "plt.plot(t,data[1,:],label = '狐狸数量曲线')\n",
    "plt.legend(loc ='best')\n",
    "plt.show()#可以看到，兔子与狐狸的数量在不断的动态平衡当中\n",
    "def f(z):\n",
    "#转换为标准的浮点数列表\n",
    "    z1, z2 = z.tolist()\n",
    "    return[0.2*z1-0.005*z1*z2,\n",
    "           -0.5*z2+0.01*z1*z2]\n",
    "result = fsolve(f, [100,100])\n",
    "print(result)#(dx/dt=0,dy/dt=0，同时满足)初始平衡，兔子种群为50，狐狸种群为40(什么时间达到，还未知)\n",
    "print('100个周期内兔子的最大值为：{},最小值为：{}'.format(data[0,:].max(),data[0,:].min()))\n",
    "print('100个周期内狐狸的最大值为：{},最小值为：{}'.format(data[1,:].max(),data[1,:].min()))\n",
    "#第一次最大值出现的\n",
    "print('兔子数量第一次达到最大值为的时间为：{},第一次达到最小值的时间为：{}'.format(np.argmax(data[0,1:30])+2,np.argmin(data[0,:20])))\n",
    "print('狐狸数量第一次达到最大值为：{},第一次达到最小值时间为：{}'.format(np.argmax(data[1,:20])+1,np.argmin(data[1,:20]+1)))\n",
    "'''\n",
    "兔子与狐狸之间动态平衡\n",
    "可以尝试时间轴放大，以及放大初始种群数量,来看整体的变化情况\n",
    "'''"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 9.99900000e+03  1.00000000e+00  1.00000000e+00  0.00000000e+00]\n",
      " [ 9.99589880e+03  3.92584509e+00  1.10149741e+00  7.38569199e-02]\n",
      " [ 9.99219050e+03  7.23943264e+00  1.40786689e+00  1.62202452e-01]\n",
      " ...\n",
      " [-4.90732291e-14  2.17401783e-07  5.33130763e-06  1.00010000e+04]\n",
      " [-4.90732290e-14  2.02416768e-07  4.97830645e-06  1.00010000e+04]\n",
      " [-4.90732290e-14  1.88462527e-07  4.64859587e-06  1.00010000e+04]]\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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yuI/XwJCAluajwEAHhjfegOxsOProgb2uUu34/X48utR7yvN4PAk19WlgSIAzHBj8dQMcGObNg+OPB5drYK+rVCf0SSH1Jfo70sCQgKQ0JW3aBOvW6aQ2pVS/08CQgJzSNGZ8PJqi6ZkDd9F58+yv3/zmwF1Tqf3Y66+/zueff97tPnPnzmXRokUDVKOBo4EhAS6vxdAjvaTnOQbuom+/DYWFcPDBA3dNpfZTq1at4vrrr6ewsLDb/YYNG8YPfvCDhDp4U5kGhgSEAoaVf6mmYnHjwFzQGPuJ4ZvfBG3XVapXFi5cyOGHH05WVhbHHXcc69ev77DP1VdfzSOPPEJRUVG35zrkkEO45ZZbuOWWW+Kux5o1a/jmN79JVlYWU6dO5bPPPosq37hxIyJCZWVl67Ynn3wSEWkddXT88cezfPnyuK/dEw0MiRCYd9k2NrxSMzDXW7UKtm/X/gWleqmxsZHvfOc7XH755axcuZLi4mIuu+yyqH3mzZtHTk4O06dPj9p+/PHH8+STT3Y458UXX8zSpUvZuHFjXHWZMWMGxxxzDKtWreLEE0/knHPOIRjseXHO8ePHU11dzbJlyxg2bBgzZszAGBPXtXuigSEBlkNwemTgRiW9/bb9VfsXlOqVFStWUFlZyZVXXskBBxzArbfeisPhiPpAfumll7joootiPqeIcN555/HSSy/FfMyuXbv48ssv+a//+i+KioqYNWsWI0aMoKKiosdjLcsiNzeX0aNHc++99/LVV1+xdevWmK8dC535nCBXpoW/PjpKBxuDmIDBmdXHt3XePCgpgdGj+/a8SvWxfx7fsVmm9JwcJv04H39DiFdP29ih/KBL8hh/SR6NlQHeOHtzh/KJP8pn7Lk51G5p5q2Loj8Az3o3vv8TxcXFpKWlcfvttzNr1izGjh3L2y1/eIV98cUXUU1DV1xxBY8//jgA7733HpdeeikXX3xx1NPDkUceyWOPPRZzPXJzcxkyZAi//OUvue+++8jKyuLdd9+N62cB8Hq9ADQ09G2qYX1iSJAzw4qa4NZc0cz6mavZ+sCmvr1QMAjvvqtPC0r1gYKCAp5//nkeeOABxowZw2OPPdahGaa8vJwhQ4a0vn/ggQeorq7mmGOO4aGHHqK6upqHH3446pjCwsIOHdDXX389ubm5HV5XXXUVDoeDl156iTfeeIPi4mLuvvvuuCeiGWO4//77GTp0KKP6eO00fWJIkCvDimpK2vNhFQAmaAgFQljOPoq5y5dDdTUcd1zfnE+pftTdX/Aur9VtuWews9vyrBFpcT8hdOa73/0uJ5xwAg888AD/8z//w8cff8wTTzzRWp6RkUFdXR2DBg2y6+Xx4PF4cDqdeL1ecnNzO5yzrq6OzMzo4euzZs3i2muv7bBvy37HHHMMa9eu5YknnmD27Nm8+eabvPHGGzgc3Y92XLlyJbm5ufh8PvLy8nj22WdJ6+MUv/rEkKBTXy7m2AeHtb5vrmjGXeRm1M9L+y4oAMyfb3/9+tf77pxK7afKyspYu3YtWVlZzJw5k3feeYennnoqar7CyJEjWbduXVznXbduHcXFxVHb8vPzKSkp6fAaPHgwu3btYvny5bjdbn70ox/x6aefsmDBAl555ZUer1VaWsqSJUu45JJLmDhxIif0w6AUDQwJyi11kzG8bWkK/y4/rnw7aptQH44QmD8fhg7VZbaV6gP/93//x6WXXtr6/vDDDyc3N5fq6urWbSeffHKnH9CWZXU5+mfOnDmcdtppMdfj/fff55RTTml9X1JSwtixY6Pq0RWXy0VJSQmzZ8/mww8/5KOPPor5urHSwJCgja/VsvIv9i/RhAyBXX5cg9PY/vQ2tj7Uh/0M8+fDMcfo/AWl+sCJJ57Ip59+yjPPPENZWRl33303lmUxderU1n3OOecc/vrXv7Jr166oY0tLS3n77bfZvn078+bNw+fzAbB69WqWLl3K8ccfH3M9jjnmGPbs2cM999xDWVkZzz77LCtXrozrHEOHDuXqq69m9uzZMR8TKw0MCfrqmd0s/rU9tCywO4AJGlyDXXgP9JI5MatvLrJtG2zcqM1ISvWRiRMn8swzz3DnnXcyduxYXnrpJebMmUNOTk7rPoMGDeJnP/sZV111VdQTws9//nM2btzIyJEjueKKKwgEAvh8Pi677DJ++9vf4nTG3mVbWFjIyy+/zPPPP8/YsWP5zW9+w9/+9jdGxzny8Oabb+ajjz5ifkuTcx+Rvp4YkQzTpk0zA71eyduXbWXrm3VcvOUgGtbUs+3hzRT9uBjv2Iy+u8iLL8K558Knn8Lhh/fdeZXqpZUrVzJ+/PhkV6NfXXnllZx11lmceuqpXe7zyCOPUFVVxaxZswawZvHp7nclIp8ZY6a1395no5JE5DfABGPMd8LvJwJ/AUqBPwM3mXAUEpHjgEeBAuAuY8zvI85zNvA7wAXcYIx5oa/q2JdcXotAox1U/VX2MDNXnt3nEKwPIE4Ly93LB7L588HrhcmTe3cepVTcHn30USyr+//DV111VY/77I365CcSkUOAHwP/HX7vBuYAnwDTgEnAJeGyAuAV4GngaOCHIjI9XDYReBa4FTgFuENExvVFHfuaw2MRaLCHq3rGeBly/jAc2U6ad/pY/79rqFtW2/uLzJ8PX/ua5l9QKgli+cDfF4MC9EFgEBEL+BNwrzGmZdrjqYAXuNEYsw64Bbg8XHYhsMEY8ytjzGrgtoiyK4A3jDFPGWO+AB4AYp+bPoCcXiHQaDDGkDY4jewjcrHSLJz5LhDwVzT37gJ1dbBkid3xrJRSA6gvwt3VwERgo4icEX5aOBSYb4zxhfdZCkwIf38oMC/i+AXA1BjKoojIlSKySEQWxbK+SF+b/D+DuWS7/TDjK2uiaYu90qrltHBkOwlUx59OL8qCBfasZw0MSqkB1qvAICKZwO3ABmAk8D/AR0BueBsA4b6FoIjkAdmRZUANMDz8fXdlUYwxfzLGTDPGTCsoKOjNj5EQd66DjKEuRISquZXsfK6stcyV52rtd0jYRx/ZQ1SPOqqXNVVKqfj0tvP5e0AGMN0YUykiTuBL4AdA+xWlmrCblwKAr5Pt9FCWUiqXNrLuHzUcet1g8k8rINjYtjyGM8+Fb3MvczUsWADjx0PEMDqllBoIvW1KOgBYaIypBDDGBIAvgMHYI44iZQHNQFW7spbt9FCWUqqW+1j0iwoaywOkDXHjKfG0lrkGufDv9ic+A9oYWLgQjjiij2qrlFKx621g2ErHv+hHAjcCrW0gIjIKcGN/8C+MLAOmANvC33dXllKcXvvWBRpD1C7e09rHAPYTA0EI1gQSO/nmzVBernMXlEqiZ555hs2bOy4DHum5556LO0HP3qC3geE14EAR+bGIHCAi1wKTgX8BhSJyQXi/mcBbxpgg9lDV6SJyrIi4gJuAueH9XgIuEpGDwv0X10aUpRSnx16iItBg2PnX7dQubsvm5hpkDy9NuJ9h4UL7qz4xKJUU7733Hr///e/Jy8vrdr/CwkJmzJhBY+MApfkdIL0KDMaYXcBp2ENKVwPXAecZY9ZiDz19TEQqgDOBm8PHVAI3AG8CO4FxwB3hsqXAg8ASoAwIAtELn6eIlicGf10A4zc4MtqWym0NDImOTFq4ENLS4JBDel1PpVSbd999tzVncuQrUnNzMz/5yU/461//SlZW98vbnHjiiXznO9/hnnvuibsuPeWefvfddzss5X3bbbe11jk7O5szzjiDLVu2xH3tnvR6uKoxZr4x5ihjjNcYM9oY83J4+yvAGOyJbeONMSsijnkUOAh7TsMhxpidEWWzgMOAGcDRxpiUDMWtTUl77JSADm9bYHDmucg/rQD3cHdiJ//0Uzj0UDs4KKX6VEZGBtXV1VGvSM8++ywnnHAC48ZFz60tKSnpNMvazTffzDPPPBNXFrVYck935eSTT6a6upoFCxZQV1fH5Zdf3vNBcerXaXvGmB3GmNfCTxbtyzYYY/5tjKnrpGyFMeZNY0xKdjwDDD40nf+qGc+wI9MBsCICg5VmMejEwbiHpcd/4mAQPvtMm5GU6kfts6pFijfns8fj4aSTTuLf//53zMfEknu6K06nk9zcXMaPH89dd93Fu+++G9Nx8dAMbgmynEJaloPGCnvkkeWJjrGBmgDB+iDuYXE+NXz1FdTWasez2ittfbDnJeczDs4kb3p+6/7ZR+SQfUQuwboA25/seaxJ5P6OzL7/CFu5cmXUMtzf+ta3WvNCT58+HYDZs2dz2223te5z5JFHsnTpUmbMmBHTNWLJPR0Lr9dLIBDA7/f3mPktHvvmQh8DwF8f4sMbtlOxyH58tNzRv5SKf+xg+5NbOzu0e9rxrFS/qq+vj3pauPjii6PKQ6FQVL/Dv/71L6qrqxkxYgRz5syhurqaW265JeqYznI+n3322Z3mfL7zzjtjyj3dE7/fz4MPPsiUKVNIT0+gdaIb+sSQIBMyLP39LnJuzyUdsNzRHVi5x+djfKHOD+7Op59CVhaMS8m1A5Xq1gE/HZnw/o5MZ1zHJ/q04PV6WbJkSev7jIzul8pvKbcsi8zMzJhzPj/00EOdjlZqOb6n3NNdmTt3Lrm5uTQ2NlJcXMzf//73Ho+JlwaGBDnDTUeh8Id/+yeGyAlvcVm4EKZNg3101Ualkk1EKCkp6bI8Ly+PiooK4llqp7Ocz0OGDOly/7KyMhoaGigtLWXmzJmceOKJHHnkkVxzzTVMmTKl22sde+yxPP7441xzzTUMGzaMQw89NOZ6xko/fRJkOQUrTQg1twSG6FsZbAxSt6yWwJ44hqw2N8PSpdq/oFQSDUTO51hyT3fF4/FQUlLCL3/5S5566ik2berDVMJhGhh6weUVGppdHHDNyI6dz1V+tj++lcb1cYy2Xb7cDg6HHdbHNVVKRdq9e3fUKxBoW6Xg8ssv595776W5OXpQZGlpKf/5z3/Yvn07b775Zuv2d955h/T0dEpLS2O+fiy5p3syefJkTj/9dO64446Yj4mVBoZecHot/M2CZ7QXsaL7GJzhSW5xLb/9+ef21x4eJZVSiauvrycvLy/q9dZbb7WWjx07ljPOOKNDB/Nvf/tbXn/9dYqLi1tTeVZVVXHttddy7733xlWHWHJPx+K2227j6aef7vNlOTTncy+YkKFpQyOB2gBZk7M7lK/7f1+RNS2HwhlDYzvhNdfAk0/Cnj3ax6BS2r6e8zkYDHLGGWdw9913c/DBB3e53y233MLEiRP5wQ9+MIC1i09Scz7vj8QS9nyym8b1DZ0GBuegOPMyLFliz3jWoKBUUjkcDubMmdNj6s677rprn0zvue/9RANo8W8q2L6t6yF2rkGu2JuSQiE7MGgzklIpQXM+q4RsfqOOja/V4cpzdVruDGdyi6m5bt06O8+zBgalVJJpYOgFh0fIyQ5Qu6Sm03LXIBfGFyLUEMNEN+14VkqlCA0MveDyWgweGqTu884DgzMvjuW3P/8cXC7opqNLKaUGggaGXnB4BMsBkt75bWxpYgpUxbBI7Oefw4QJutS2UirpNDD0gjvPgcPZcdZzi7Shbop+UoyntPu1WDDGDgzajKRUytDUnioh37h/GE5314HBSrPwlmZEJfHp1Pbtdo5nDQxKpQRN7akSZvwGQl0HBoD6VXXUfVnb/Ym041mpAdVZ2swWmtpTA0OvbPjXHvsbZ9e3cff7VVTNrej+RC1LAPfDKolKqfhoak8NDL1StyHcqdzNXRxy7jCKelpj/ssvYdQoyO44e1opNbA0tacGhl5xhgcQhYx0vU+OC0d6D30My5frMFWlUkRnqT1FhE2bNjF9+nREJCqtJ7Sl9oxVZGrP5ubm1tSe8abnjEzt2Zd0raRecIQnPJtuAkNzZTM1H+8m5+t5nc+Qbm6GVavg29/up1oqNTDWXLeGuiV1A3rNzMmZjL1vbJ+es7PUnn6/n0MOOYSHH36Yr3/96x1SaRYWFjJ//vyobWeffXbUqq0tfvaznzFr1iyef/55LrvsMp544gluvfVWrrjiiqjr9kRTe6Yox2A3790c5LuXdD33IFgXpHreLjyjPZ0HhjVrIBCAiRP7saZKqURpak8Vl/RBTlz5LqSbhbRcefYt7nL28/Ll9ldtSlJ7ub7+yz1ZNLWn9jH0SsGBDr79x0Hkje18ET0AR5YTcQiBrpbfXrbMXmb7oIP6qZZKqXhoak8NDL3StLmRqrmVmG4GBIgldl6GXd0EhrFjoY/bCJVSidHUnhoYesUqzmTVynS2L+x+1qNrsIvmyi7WS9IRSUqlFE3tCRhj9vrX1KlTTTJUr2kyD/KlWfVMdbf7lf9jh1lz00oTCoWiCxobjbEsY269tf8qqVQ/WLFiRbKr0K8CgYA57bTTzLJly7rd7+abbzbPPPPMANUqMd39roBFppPP1D57YhCRN0TkkvD3E0VkoYhUi8g9EjEGS0SOE5GVIlIpIte3O8fZIrJJRMpE5Py+qlt/aV5Xx9ivC4Ee8i24ClyYZkNwTyC6YNUqO3ObPjEolVJaUnt2l+8Z7NSeqZzvOVF9EhhE5ELg5PD3bmAO8AkwDZgEXBIuKwBeAZ4GjgZ+KCLTw2UTgWeBW4FTgDtEJHpOeorxb2tk6Fgh0Nh9YEgrcAPQXNGuOWnZMvurDlVVKuVoas9eEJFBwO+Ar8KbTgW8wI3GmHXALUDLYh4XAhuMMb8yxqwGbosouwJ4wxjzlDHmC+ABIPZ56ckQNASaIdDQfepOV6E9zyGwu90Tw7JldnKesfvGMD+l1L6hL8Ld74B/Yj8hABwKzDfG+MLvlwITIsrmRRy7AJgaQ1lKMv4Q4hLcud3fRmeukzG/GUf24e06lpYvh3Hj7OCglFIpoleBIdwMdAJwU8TmbGBDy5twB0dQRPLalwE1wPDOjmtX1tm1rxSRRSKyqKKih9VL+0nIF6LwaxlM/FF+t/uJCFZaJ7d62TJtRlJKpZyEA4OIpAN/BH5kjIlMOBAAfO12b8JuXmpf1rK9s+MiyzowxvzJGDPNGDMtnhmKfcn4Qt3mYohU8+luyv+2vW1DXR1s3Kgdz0qplNObJ4afAwuNMa+1214FtP+kzgKaOylr2d7ZcZFlKSnkC1H2cSOf3razx339VX6atjS1zZxcscL+qk8MSqkU05vAcAFwpojsFpHd4fcPA7OBo1p2EpFRgBv7g39hZBkwBdgW/r67spQU8oVorAxSvbL9A1JH+acUUHz9qLbVE3VEklIpTXM+J+YbwERgcvj1CvZQ0wOBQhG5ILzfTOAtY0wwvM90ETlWRFzYfRNzw/u9BFwkIgeJSCZwbURZyjHGEPKFMCI9jkrq1PLl9jIYo0b1feWUUr2iOZ8TZIzZaozZ2PIC6oBKY8xW7KGnj4lIBXAmcHP4mErgBuBNYCcwDrgjXLYUeBBYApQBQewnkJRkAgYEsAR/DxPcAEL+EFsf3MSej8KLZC1bBhMmQJyJOZRSiXvyySdbcyZ7vV6OP/54lrescBymOZ/7cK0kY8wlxpgnw9+/AozBntg23hizImK/R4GDsOc0HGKM2RlRNgs4DJgBHG2MSdkwbLksxv52PNV7nD3OfG7Zv7ncR9Pm8I+0bJl2PCuVBOPHj6e6upply5YxbNgwZsyYEbVqquZ87sdF9IwxO4wxrxljdnVStsEY829jTId0T8aYFcaYN40xKd3x3CL/UC+DJrhj29my2PNJDaHyXVBWpv0LSiWBZVnk5uYyevRo7r33Xr766iu2bt3aWq45nzVRT8L8Vc3smlvJtOsG4S7qfsnsYFOQVT9cRcXf7PkWvmffYRJoYFD7luuugyVLBvaakyfDffclfLjXa4+Ij/xrv7Ocz2+//TYA06dPB2D27NlReZ9bcj7PmDEjputG5nyeNWtWa87nROrfkvM53nzR3dk3F/oYAMH6II1r6gk29hypv7r8Kyr+VsHQy4aQd1oOmS47sUblpq4zPCml+pcxhvvvv5+hQ4cyKmIQSGc5n6urqxkxYgRz5syhurq6w5LchYWFlJeXR207++yzyc3N7fC68847KSgo4Pnnn+eBBx5gzJgxPPbYY10mAeqK5nxOQekjPIy6dSyf/bqC9f/cwfcXjOl0v6q3qih/vpyS20oYclEhWx/YRFFGFcGXvKz4nzqmHFlL1pTuO7iU2iv04i/3gbRy5Upyc3Px+Xzk5eXx7LPPkpbWdd72/THnsz4x9JKvKsiuL5q6LN9460bSS9IpvqWYtGF2X4SsXoFMmYQz38WqS1YR8vfcea2U6hulpaUsWbKESy65hIkTJ3LCCSdElbfkfI5HVzmfS0pKOrxyc3MpKytj7dq1ZGVlMXPmTN555x2eeuopPv/88x6vdeyxx7JkyRJOOukkpk+frjmfU0n98lq2/XEzrnRDsMlgQh0fA+uW1lHzcQ1F/12E5bZweBw4cpxYG1ZhTZ7IgQ8fSP0X9Wy5p++HmymlOudyuSgpKWH27Nl8+OGHfPTRR1HlmvNZA0PCmiv9NKyqx+G1b2GgqeM/mB1P7kDcwtAfDm3d5vHW4qjZBRMnMvjMwRR8v4CNv9hI4/qUHZmr1D5p6NChXH311cyePTtqu+Z81sCQMOOzm3+cXnskQPu5DMYYKl+uZNCJg3ANaltWO9MRju7hOQyl95UilrDh5xtQSg2sm2++mY8++oj58+e3btOcz2jO50RVvLLTrLlxpdnwWo2Zc9oG01DhjyqvXVpr3uEds+2xbdEH/uEPxoAxZWWtm9bNXGfe4R1Ts7hmIKquVK9pzmfbvprzWUclJSgUXnK75LQsSk7rOKqoam4VAPmnt8vVsGwZZtAgzODC1se14puKKXu0jA0zN3DIvw/p55orpXrSkvO5p9Sdd9111z6Z3nPf+4kGSMgXQrrJxbDn/T14xnlwD4ueFW2WLcOXNZpdr1e2bnPmOCm+qZiqN6qoWVTTb3VWSsVOcz6ruIV8QSy3RdmH9Tx5wCp2fto2c9IEDbs/2E3usbnRBxmDLF8OkybiGR2dg2j4j4bjzHWy+a7ul/lVSqn+poEhQaGmEFa6ffvqtwVormnrfK5fXk9wT5Ccb7TrSNq2DfbsIf2UaWROim5+cmY7Kbq2iMp/VlK/vL7f669Ub5k4Z+qqgZfo70gDQ4JaAoPTEx6uGjEqqXaRnek0+2vZ0QeFl/c1Bx9Mc2Uzwabo5TQOuPYArAyLzb/WpwaV2lwu1z6Xg2Bf1NjYiMvl6nnHdjQwJMiR4cA1yIXTa6+pEhUYPqvFkeXAU+qJPiictc2XN4ZNd66jYVX0k4Er38Xwq4ez84WdOq9BpbTCwkK2bdtGQ0ODPjmkIGMMDQ0NbNu2jcLCwriP11FJCSq6yp7+XrPJngTjj8jiVre4jswpmYgl0QctWwZDhpB2cBE4vsK3rYmsydFPFSNuGMG2B7ax5XdbOPChA/v3h1AqQdnZ9r/bsrIy/H5/kmujOuNyuRgyZEjr7yoeGhh6yZ3jYMz3s8kqth/XQoEQdUvrGH718I47L18OEydiOS3cw9Jp2tTxqcA9zM3QHw5lxxM7KJldQlph14t7KZVM2dnZCX3oqNSnTUkJMEHD1gc3Ubt4D+5cB6e8WMyIb9krKzZtbCLUGCJjUkb0QaGQHRjCM57TSzw0bW7qdI2lETeOIOQLse3Bbf3+syilVHsaGBJgAl23qTassoeteg+KHo7Kxo3Q0NCanCe9xIPxhWje7utwDu84L4O/O5htD24jUBfos3orpVQsNDAkwHJbHPDTkWQdZg9HfWLoKj75Xzt1dWtgGNcuMLQkHA8HBk+J3THduLHzTubim4sJVAfY/uftfV19pZTqlgaGPhDyhWiusYeeNqxqwFXoilo4D2gdkcSECQA4B7lwZDlo6iIwZH8tm5xjc9j6+62ar0EpNaA0MCSgaVMjG+9a19p57PRaBMKjkhpWNXRsRgL7iWHECAivnigipJd4adrY0HHfsOKbi/Ft8VH+1/Iu91FKqb6mgSEBwboA/oq2tdqdXotAo/1XfZeBYdmy1o7nFp4SD/5KP4HazvsRBp06iIyJGWy5e4uOFVdKDRgNDAkINtlBoGVJDKdHCDSEaK5sJrAr0DEwBAKwcmVr/0KLzMnZFP2kGMvT+a9BRBhx0wjql9VT9e+qvv9BlFKqExoYEhBqFxhKz8nhgBMyafzKblrqEBjWrYPm5g6BwTXIhbc0A8vZ9a+h8LxC3CPcbL5bl8lQSg0MDQwJaAsMdva2af9byCE/ze96qGpLx3O7piSApi2NVL+zq8trWS6LA64/gD3v7aFmgS7JrZTqfxoYEhDyBUFA0tqWvAgFDQ2rGrDSLdKL06MPWLYMRGD8+A7naljdQOVr5QQbgh3KWgy7YhjOPKc+NSilBoQuiZGAUEMIy+NAxA4Mc8/dzK4vfUwqbcIz1oM42q2RtHw5jB4NGRkdzpVzdC65X8/D6ibpjzPTSdFPith05yYavmroOEdCKaX6kD4xJCDYGMThbbt1jnSLQEOIxnWNeMZ4Oh7QyYik1mM9jm6DQouia4qw3BZbfrsl4XorpVQseh0YRORMEVkvIgERWSoiE8PbJ4rIQhGpFpF7pOXPa7vsOBFZKSKVInJ9u/OdLSKbRKRMRM7vbf36Q6ghiOV1tL63RyUFadrQRProds1IPh+sXt2h4zlS7ec1bH9ya7fXTCtMY+ilQ9nx9A58nSyjoZRSfaVXgUFExgBPAjOB4cAS4HERcQNzgE+AacAk4JLwMQXAK8DTwNHAD0VkerhsIvAscCtwCnCHiIzrTR37Q9pQN56StuYcp9fC1AcJNYZIH9UuMKxcCcEgHHJIl+cL1geoW1pLc3n3H/gjbhiBCRi23t99EFFKqd7o7RPDeOAWY8xfjTHlwEPYgeBUwAvcaIxZB9wCXB4+5kJggzHmV8aY1cBtEWVXAG8YY54yxnwBPABc1Ms69rmCM4dQcNaQ1vdOr4XVaE9S84xu15T05Zf210mTujxfxgQ7zWf98rpur+sZ46Hg7ALKHikjUKOL6yml+kevAoMx5lVjzB8jNk0A1gKHAvONMS1/Ai8NlxEumxdxzAJgagxlUUTkShFZJCKLKioqevNj9Nrwb3gpPc1+gujQlPTll5CWBmPHdnm8a5CLtOHuHgMDQPFNxQRrgpQ9WtarOiulVFf6rPNZRJzAz4BHgWxgQ0uZsddzCIpIXvsyoAa7GYoeyqIYY/5kjJlmjJlWUFDQVz9Gj4wxbPjFWna/3zYTufjkLEZ8zQ1AekkngWH8eOgh72rGwZk0bmjodtgqQNbULPJOymPLb7foktxKqX7Rl6OSZoW/PgwEgPYN5k3YzUvty1q200NZagiCd6wXZ17bB30oYKhf1Uja8DQc6Y7o/b/8sttmpBYZE7IgBA2ren5qGPXLUfgr/Gy7XxP5KKX6Xp8EBhH5BnADcF64+agKaP9nfBbQ3ElZy3Z6KEsJ4hSGnD+czElZrdvWvLCbjc/vwjXcHb1zdTVs2xZTYEgvTseR6aDuy9oe980+Ipv8M/LZfM9m/NWab1cp1bf6YrjqSOBF4BpjTLinlYXAURH7jALc2B/8UWXAFGBbZ8e1K0sJJmQ6rHTqynbgIoRzSLvAEEPHcwuxhMxDs6hfUUfI13P+hVG/HEVwT5Atv9N5DUqpvtXb4aoe4DXgVeAlEckUkUzgA6BQRC4I7zoTeMsYE8QeqjpdRI4VERdwEzA3vN9LwEUiclD4PNdGlKWExrUNrL1xFY0b2vIouNLBRQjH4Hb9CHEEBoCsKTmYZkP98p6fGjIPyaTg3AK23reV5p0p9VCllNrL9faJ4STgYOxhprURr6LwtsdEpAI4E7gZwBhTid3s9CawExgH3BEuWwo8iD0fogwIYvdZpIxgQxBCRM1WloYAAkhuWvTOX34JublQVBTTudNHecg+Mhdn++xvXRj1y1EYn2HDzzf0vLNSSsWoV2slGWP+BUgXxRvDE+CmAp8YY3ZFHPeoiMwFDgI+MMbURZTNEpHnsIPLe8aYlPpzOFhvjxpyZLR1Mod2h9v5szp5Ypg0yV5ALwZiCUPOHRZzXbxjvRT9tIitf9hK0U+KyDw0M+ZjlVKqK/26VpIxZocx5rXIoBBRtsEY8+/IoBBRtsIY82aqBQWAYDjbmiOzLaaaKruag7/R1iGNMfYaSTE2I0VqrmhuTRvak5G3jsSZ62Tt9Ws1y5tSqk/oInpxCtbZ6yRFrqDqL/NheSyGfiu7bcfNm6GmptulMLqy/cmtVPxzR0z7uvJclNxewu55u9n1Std5HZRSKlYaGOIUrA3gzIqeq9C4thH3yHSadkVMTouz4znSkHOHMezSA2Lef/hVw/GO97L2urWtTV1KKZUoDQxxCtQGcGRFd800rm2kcn2QT28rb9v4+ed230ICgSG92IMzJ7YOaLCzvB346IE0bWxi4+0b476eUkpF0sAQp2BdEEdm2xODCRma1jcR9Dhpron4a33xYjjwQMjK6uQsPWva1EjZY1sINsb2BJB7bC5DLx/Klt9voXZJz8NdlVKqKxoY4hRs98TgK/PZOaCzXDTviZiY9tlncNhhiV/IgvoVddR8vDvmQ8bcPQZXvovVV67GBLUjWimVGA0McTDGkH14Dt7StuWbmtY1ASB5rrYnhooK2LIFpna6MGxM0kd48Iz1Uv1+FSYQ24e8a5CL0vtKqV1Yq/mhlVIJ08AQBxGh4HtDyTykbfRR41p7WKmj0E1zTfiJYfFi+2tvnhiAvG/mE9wToHbxnpiPKTyvkIJzCth460ZqFtX06vpKqf2TBoY4hAIhQv7odYwa1zYiLmH8tYUcdtNge+Nnn9lfexkYvOMycBe5qXqzMuamIRHhwEcPJG1oGisvXKmjlJRScdPAEIf65XWsu+krfGVNrdsa1zWSXpLOqDOyGXterr1x8WIoLYWcnF5dT0TIP7UAf6WfmgW7Yz7OlefioKcPonFNI2uuXaMT35RScdHAEIe0IW4GnTI4ai2jxrWNeEo9NFUFKF/UaH8I97bjOYJ3QibpozzsmltJqLnnVVdb5E3Po3hmMTue2MH2P23vk7oopfYPGhji4B7qJv/kgtZkPMYYGtfZgWHlX3bzt8PX0bx+J2zc2KuO50giwuBvFxKsCVD9dnwzm0fdPopBpw5izTVr2DM/9n4KpdT+TQNDHJormgnUtqXTbN7ZTLAmiGesB2+hHSwC//nALjzmmD67rme0l8zDsqlZtIdQIPanBnEI458fT/rIdJafvZymzU09H6SU2u9pYIjDjqe3sfP5stb39cvqAcg4OIP0Antug/lgPrjdMG1an1678KwhFP9sFJYzvl+ZK9fFxJcnEmwMsvSkpTRXpty6hEqpFKOBIQ6Ban9UrufWwDAxA084MDgXfwSHH24Hhz7kyHTiSHdgAobGjbGtvNoi4+AMJs2ZhG+Tjy9P/5JAXaDng5RS+y0NDDEK+UIE64O4IjqeG5Y34BrsIq0wDU+hAyeNpK1dAl//er/Vo3LOTrY9vIlATXwf7rnfyGXC/02g9rNalp2xTIODUqpLGhhi1LzTB9gjk1rUL6vHe7A9C9o7xMkp/28nVtDfr4Eh75v5DL2oCGd2/DmWBp8xmPFPjWf3+7v54qQv8LckGFJKqQgaGGLUvKMlMNjpO0OBEHVf1JF5iJ01zZFmMTJjqb3z0Uf3Wz2cOS4yJ9kL8/m2+zCh+OYoDLlwCAe/eDC1i2pZ+s2l+Lb7+qOaSqm9mAaGGDXv8CEOwZVvB4aGlQ2EGkJkf61teYzmV98hMHoC5OX1e318ZU1s/t16KueUxz2BreB7BUz810Qavmpg8RGLqV2sq7EqpdpoYIiRb4cP15C01sxttZ/aH6ZZh4eX1W5owLHgAzYFjhyQ+qQNc5NzVB67362i6s3KuI/PPzWfKfOngMDnX/+cnS/s7IdaKqX2RhoYYtS83RfVv1CzsAZnrhNPqcfe8O67OEwzm61vDEh9RISCs4aQNS2Hqn9XUvla/E8OWZOzmLpwKpmHZbLygpWsvGRl1DwNpdT+SQNDDPzVfgK7A3hKPK3bdr+7m+yjshErnPv51VcJOj2s23nIgK1NJJYw5PxhZB+VS/Vbu9j5wva4ls0Au89k8ruTGXnrSHY+s5NFkxdR9WZVP9VYKbU30MAQA4fXwdBLisiYaDcbNW1povGrRvJODPclBIPw0kvUTjoJX2MaDdsH7q9usYTC7w9l0MmDqV24h61/2Ig/zklsltNi1O2jmPL+FMQSvjjpC1acvwJfmXZMK7U/0sAQA8ttkXVoduschuo3qwHaAsN770F5Of7TvgfAnrUDO7tYRMg/pYDhVxyAv8rP5t9toHZJ/LkYco7JYdqX0yi5rYSKf1awoHQB625eh79Kh7UqtT/RwNADYwzV7+zCX9X2YV/xUgXuEW4yDs6wN/z5z5CTQ/aPz+KMt0rIPzQ9KXXNODiL4htG4S5Kx/LYv9p4m7Uc6Q5KZpdwxIojKJhRwJZ7tvDJqE9Ye8NaGjfEN+NaKbV30sDQg+YdPirnlNO4rsF+v7OZqrlVDLlwCCICO3fC3/8OP/wh7uFZjDghE3eOI2n1deWnUfSTYjLG2fMrds0pZ/vT2+Ke7+AZ7WH8M+OZ9sU08k/LZ9sftrGgdAHLZixj1xu74lrMTym1d4l/+ux+xj0snVG3lmJ57A/7ssfKIAhDLhpi7/Cb39h9DD/9KQA7PmmgaoWPCZf1/1yGrohI6/eWx4HDb1o7yRtW1+MZ420ddtuTzImZTHhhAk33NFH2cBllfyyj8h+VuApcFJxTQOH3C8k+OhvLpX9jKLWvkH0hu9e0adPMokWL+vy8JmiiPkD9u/0sGL2AnK/nMOmVSbBqFUyeDOefD3/5CwDvX1PGyseruaJ6PA53an1Y+rb72Hz3eiyvRcaELDIPycI7LgMrLfZ6hnwhqt6oYudzO9k1ZxehphCObAd5J+Qx6ORBZB+TTcb4jJgDj1IqeUTkM2NMh6WgUy4wiMhE4C9AKfBn4CbTQyX7IzAYYyj781bEKQy7uAgEVl64kvIXy5m6aCpZpQLHHWcn5Vm2DIYNA2DDnBpeP2MzZ84r4YDpmX1ap94yIUPDyjpql9RSv6KWUEMIcQju4nQ8Y7x4RntxF6XjyHJEPXV0JVAToPqtaqreqKLqjSp8W+xRTI4sB1lHZJH9tWwyD8nEO8GL90AvVooFSqX2d10FhpRqShIRNzAHeBU4D3gIuAQ7UAyYkD9ExT920rCijoKzhmD8hrXXr6X8hXJG3TGKrIIaOOVcWLIE/vWv1qAAUHR8Bo50YcWfq1MuMIglZBycRcbBWZigoXFdA/Ur62hc30D1vF1Uv2VniBtxXQnpIz00bWmkcX0jOUflYqVZhAJ2IGkJGs5sJwXfK6DgewV2Nrs1jdR8UtP62vybzRAMX9wBnlIPntEe0kem4y52kz4ynfSR6aQNTcNV4Io5ICml+ldKBQbgVMAL3GiM8YnILcCD9HNgMEFDsC6Av9JPw5p69nyyG99WH96xGVS/tYfVFy3BbN7OQd+pZsjmF2DccxAKwQsvwLe/HXWutCwHk28YzGd3VlByehYHXpDbn1VPmDgE74EZeA+0R1aFfCGatjTSXOYjbag9w7t+WR1Vb1aSe4zdX1L5r3JqFuzGkenA4XVgZThxeC0cGfZ7cVukj0pjyEVjEREa1jfQsLKBYE2QhhUN1C2po2lzEzULaghUdZzrIWmCa7ALV4GLtII0HNkOHFkOnFlO+5pZES+vA8ttIW7Bclutrw7vXWI3aznswBj1vaVBSKnOpFpgOBSYb4xpmVm1FJjQXxerPug83Gs+RkwQCCEmRCZBsgi/J4RFM6MIV2cO4PHA978Pt94KY8Z0et6p/6+AHfMbcGbYTSdb36nj3SvDmd8EROyvJz0/goLDPKx/uYZPZnVcq+jUfxSTN87N6ud3s+jOig7lZ8wtIfMAFyv+XMWSezvmg/7eh6NJz3Ow9P5Klv+pukP5uYvH4HBbLLqrnNXPReaE3oXlFM5dMobcYwexYHY561+uIWdwiKxB4HIFcXmDDJli4av24yv3IxhE7Hj5+tW7yBjm5GuXuWlcW8/GrV62zw9w4GEuckudQCah5hDBuhDBmiDBhhChRvvlrw2xa12QtK0NpLvD2+oM+EP0y8d4S+uWEP7F2D+DlW7hsAzisvDV2iOwnGlth4lFa2AxwbaWzmAQgkEhLctCQiGsNIvG6hAi4IrI3STh4IQxhIJt24MB+5We7wR/EHFbNFSEsCxwuduuYzkFscCEIBRo2x7wQzAgdqpZXxBcDhoqgzgcJqr+lksQ6Xi8v1kIBSFjiAPTFMQ4HTTuCuJwGpyuTo4PQiji52/2CSYEmUMdhBqDBMXCtzuE02VwRHzaONLC9zoYff+am+ztGUMchJqCBIIWzbUhXGkGKzzYTwSsluMDRI248zUIllPw5gshv6G5SQg0hHC52x3vCh/vbxvSbQw0NwrOdMGdJWCgqdYQ9BnS0g1itRwvWOF7EfIbWhq6TciuvyvDsvd3CPW7QpgguD2Gln/AYglW+F4Em9vqHgqC3yek5Vg4LYOVZlG3MwgSPr7l3luCOAEDxmExdf4UPKPbVmXoC6kWGLKBDS1vjDFGRIIikmeMifpkE5ErgSsBiouLE7qYjBqJr6oKHA5wOhCXE0l3IR4XjiwXVnYaaSMyoXgoDBkC48fDlCmQltbteV0ZFmfOK2ltFnGkCYVHeMBg/zLDv+OWwOHOtRg0oWPGN0e6fbw7z9Fpecs/7vR8Z+fl4f8InsLOy1v+oXqHujqUtzQZOTIcZAxvO74B+2dwicW0/z4AgM9/V8nOT+qRcNAbNEFIH+xk0ImDCR2Tx65na/FVu6k3QZqq7A/49EEOxlyRjQkaNr1eS3NlwP5cDgnUufCMTWPCt92YgGHZv3zUbWomx9uMIxiEoCEtQ8g70E2o2VD5eQOhRgMhQ6AZ6usdZI90kTc4hDgtti7wEWwyZKQHEGPA2Pc+fZADQoa6zX77w8XYH+qBZouMES7cjgCODAc7v7An+DndbZ/gLq+FK8uym+Qqgq2/VBMUggGL9BIXzmAAR6aTppX+8L+DoP1vAHBlWjg8FiZgaKoOn9fYx4eCQvpoF9IYQDKcNIkfEYPD1TZE2JXlwOEWgs0Gf01bvUIBCxMS0ktdUB/AeJw0WX7EMjicbcen5TiwnELQF8Jf17Y9GLAgJKQf6MLUBAi6HPgcASyHweGIOD7PgWUJgcYQgYa27ZbfwhjBM85FcHcAv+XAv63j8e58B4Lgrw8RbGrbLs0OEOzj9wTwBRwEygNYzhAOK3zzROzfHdBcGyQU/nA1gJXpwJEmeEY6CDWFMLVCaHcQhzOEFT5eHII71z7etyeICbQEBsHyWzgyLTwFgjHgLzeYhhCWK4Ql9n6WS0jLDh9fHWwNTKGQYAUsnIMcpGfaf1Q0Ou3zW64QEj7e4bZwZdr/95t2RTw5h49PG+okzRHEkeGgwQTa/u2EOTwWLq+FCRlCDke/9N2lVOeziPwGCBpjZkZs2wIcaYzZ1tVx/TUqSSml9mVddT6n2jCRKqCg3bYsQDPYK6XUAEm1wLAQOKrljYiMAtzYAUMppdQASLXA8D5QKCIXhN/PBN4yxgS7OUYppVQfSqnOZ2NMQESuAF4Qkfux+5OOT26tlFJq/5JSgQHAGPOKiIwBpgKfGGM6jsNUSinVb1IuMAAYY3YAryW7HkoptT9KtT4GpZRSSaaBQSmlVJSUmuCWKBGpADYlePhgoLIPq7M/03vZt/R+9h29l50baYxpP3ds3wgMvSEiizqb+afip/eyb+n97Dt6L+OjTUlKKaWiaGBQSikVRQMD/CnZFdiH6L3sW3o/+47eyzjs930MSimloukTg1JKqSgaGJRSez0RyRWRr4lIXrLrsi/YbwODiEwUkYUiUi0i94hmoe+RiKSH79nxEdsOEJG3RaRGRJ4SEXdEmd7jLojImSKyXkQCIrJURCaGt3d5z0TkOBFZKSKVInJ98mqfWkTkPGAj8Gdgm4h8P7xd72WC9svAEP7wmgN8AkwDJgGXJLNOqU5EvMCL2Pcr0otANTAFCGEvla73uBvhRSKfxL5Xw4ElwOPd3TMRKQBeAZ4GjgZ+KCLTB7jqKUdE8oEHgKONMZOAnwC/1XvZS8aY/e4FfBfYCbjD7ycDHya7Xqn8Av4C/AZ7hvnxEfetGSgMvx8MbNR73OO9/DZwVcT7I4Bgd/cMuA5YEnHMd4Fnk/2zJPsFlADnR7w/BDs1ud7LXrxScnXVAXAoMN8Y4wu/XwpMSGJ99ga/MMZsEJFzI7YdCiwzxpQDGGMqRcQnIkPQe9wlY8yr7TZNANbS/T07FJgXccwC4Ff9Wc+9gTFmI3YzEiLiAm4E/oney17ZL5uSgGxgQ8sbY//ZENSOq64ZYzZ0sjnqPobVYDeP6D2OgYg4gZ8Bj9L9PWt/r1vuswJE5DBgB3AS8FP0XvbK/hoYAoCv3bYmwJuEuuzNuruPeo9jMyv89WHiu596L6MtAU4GvgIeQ+9lr+yvgaEKaL+iYBZ2e7mKXXf3Ue9xD0TkG8ANwHnhJo947qfeywjGmJAxZhHwA2AGei97ZX8NDAuBo1reiMgowI39D0bFbiEwNdy2i4ikAwcB29B73C0RGYk9ousaY8yX4c3d3bOoMuxRYNsGprapS0ROFpE7IzY1Y+eKX4Pey4Ttr4HhfaBQRC4Iv58JvGWMCSaxTnsdY8x67I6/G8ObbgTWGGPK0HvcJRHxYKeufRV4SUQyRSQT+ICu79krwHQROTYciG8C5iah+qlmFXCtiFwqIiOAXwNvYt8vvZeJSvawqGS9gDOAeqACKAcmJLtOe8MLOxAcH/H+a9gJUCqAunZleo87v4dnYv9V2/5V0t09A67GbhuvAtYDQ5L9s6TCCzgNWIndifw3oCC8Xe9lgq/9ehE9ERkKTAU+McbsSnZ99lbhkR5HAUuNMdvalek9jlN39yzcJHIQ8IExpi4Z9dub6L1MzH4dGJRSSnW0v/YxKKWU6oIGBqWUUlE0MCillIqigUEppVQUDQxKKaWiaGBQSikV5f8DFitXpUsx95gAAAAASUVORK5CYII=\n"
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     "metadata": {
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     "output_type": "display_data"
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   ],
   "source": [
    "#8.5\n",
    "\n",
    "'''\n",
    "attentio：python解决ODEs问题，有两个函数，solve_ivp和odeint，但是两个函数然后输入y值得位置不同，错误使用则会报错\n",
    "'''\n",
    "'''\n",
    "8.3.4用的是SIR模型，SIR模型的进一步演变即为SEIR模型\n",
    "可以增加一种人群类型，即暴露者（潜伏者）类型（E类）\n",
    "变化规律为：S-->E-->I-->R，数据相互之间不影响\n",
    "\n",
    "β表示一个单位时间内感染者导致感染散播的平均传播人数\n",
    "N为总人数\n",
    "设定该病的平均潜伏周期为C天，平均传染周期为D天\n",
    "dS/dt = -(β*I(t))*(S(t)/N)       (易感人数的变化)\n",
    "dE/dt = β*I(t)*S(t)/N-1/C*E(t)   (潜伏人数变化率 = 新增加潜伏感染人数-潜伏转确诊人数)\n",
    "dI/dt = 1/C*E(t)-1/D*I(t)        (感染人数的变化 = 潜伏转确诊人数-治愈人数)\n",
    "dR/dt = 1/D*I(t)                 (康复者人数变化)\n",
    "N = S+E+I+R                      (总的人数限定)\n",
    "\n",
    "（1）β/N 可以用λ替代，λ表示平均传染接触率\n",
    "（2）1/C 可以用a来替代，a表示平均发病比例\n",
    "（3）1/D 可以用μ来替代，μ表示平均治愈比例\n",
    "化简为：\n",
    "dS/dt = -λSI     S(0) = s0\n",
    "dE/dt = λSI-aE   E(0) = e0\n",
    "dI/dt = aE-μI    I(0) = i0\n",
    "dR/dt = μI\n",
    "'''\n",
    "#查阅相关文献发现，改模型无法求解析解，只能求数值解\n",
    "#使用scipy中的odeint方法来解决\n",
    "import numpy as np\n",
    "from scipy.integrate import odeint\n",
    "import matplotlib.pyplot as plt\n",
    "N = 10000\n",
    "S_0 = 10000-1  #使用正规化人口数据,初始存在一个潜伏者，则剩下来的都是易感者\n",
    "E_0 = 1   #初始存在1一个潜伏者\n",
    "I_0 = 1     #初始存在感染者\n",
    "R_0 = 0       #初值不存在康复者\n",
    "#使用365天作为一个周期，单个体平均传播人数为3，潜伏周期为14天，传染周期为14天\n",
    "t_max = 365\n",
    "lamda = 3/10000 #λ平均传染接触率\n",
    "aerf = 1/14#a平均每天发病比例\n",
    "mu = 1/14 #μ平均每天治愈比例\n",
    "def SIER(y,t):\n",
    "    s = y[0]\n",
    "    e = y[1]\n",
    "    i = y[2]\n",
    "    r = y[3]\n",
    "    return  -lamda*s*i, lamda*s*i-aerf*e,aerf*e-mu*i,mu*i\n",
    "t = np.linspace(0,365,t_max+1)#获得101个数据点\n",
    "initial = (S_0,E_0,I_0,R_0)\n",
    "ySEIR = odeint(SIER,initial,t)\n",
    "print(ySEIR)\n",
    "plt.plot(t, ySEIR[:,0], '--', color='darkviolet', label='S(t)-SIR')\n",
    "plt.plot(t, ySEIR[:,1], '-.', color='orchid', label='E(t)-SIR')\n",
    "plt.plot(t, ySEIR[:,2], '-', color='m', label='I(t)-SIR')\n",
    "plt.plot(t, ySEIR[:,3],  color='r', label='R(t)-SIR')\n",
    "plt.legend(loc = 'best')\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 258,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#续8.5\n",
    "\n",
    "'''\n",
    "在上述条件不变的情况下，验证保持社交距离对于防控疫情的效果\n",
    "'''\n",
    "import numpy as np\n",
    "from scipy.integrate import odeint\n",
    "import matplotlib.pyplot as plt\n",
    "N = 10000\n",
    "S_0 = 9999  #使用正规化人口数据,初始存在一个潜伏者，则剩下来的都是易感者\n",
    "E_0 = 1    #初始存在1一个潜伏者\n",
    "I_0 = 1     #初始存在感染者\n",
    "R_0 = 0       #初值不存在康复者\n",
    "#使用365天作为一个周期，单个体平均传播人数为1，潜伏周期为14天，传染周期为14天\n",
    "t_max = 1000\n",
    "lamda = 1/10000 #λ平均传染接触率\n",
    "aerf = 1/14#a平均每天发病比例\n",
    "mu = 1/14 #μ平均每天治愈比例\n",
    "for dis in range(1,11):\n",
    "    soc_dis = 1/dis#0-1之间的数用于控制易感者的人数\n",
    "    def SIER(y,t):\n",
    "        s = y[0]\n",
    "        e = y[1]\n",
    "        i = y[2]\n",
    "        r = y[3]\n",
    "        return  -soc_dis*lamda*s*i, soc_dis*lamda*s*i-aerf*e,aerf*e-mu*i,mu*i\n",
    "    t = np.linspace(0,t_max,int(t_max)+1)#获得101个数据点\n",
    "    initial = (S_0,E_0,I_0,R_0)\n",
    "    ySEIR = odeint(SIER,initial,t)\n",
    "    plt.plot(t, ySEIR[:,0], '--',linewidth = 0.9)\n",
    "    plt.plot(t, ySEIR[:,2], '-')\n",
    "    if dis == 10:\n",
    "        plt.plot(t, ySEIR[:,0],'--',label = 'S(t)的变化')\n",
    "        plt.plot(t, ySEIR[:,2], '-',label = 'I(t)的变化')\n",
    "plt.legend(loc = 'best')\n",
    "plt.show()\n",
    "'''\n",
    "可见随着社交距离的扩大，易感人群逐渐稳定并保持较少人群感染。\n",
    "感染人群的波峰到来时间逐渐延后，并且波峰值更小，感染的扩散风险更小\n",
    "'''"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 262,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "线性拟合表达式：  \n",
      "1.177 x + 4.846\n",
      "1.1768383333333334\n",
      "[14.26029778 14.84871694 15.43713611 16.02555528 16.61397444 17.20239361]\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": "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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#8.6\n",
    "\n",
    "#看数据应该是一个单调增模型\n",
    "import numpy as np\n",
    "year = np.arange(0, 9, 1)\n",
    "num = [5, 5.9945, 7.0932, 8.2744, 9.5073, 10.7555, 11.9804, 13.1465, 14.2247]\n",
    "fit = np.polyfit(year, num, 1)\n",
    "print(\"线性拟合表达式：\", np.poly1d(fit))\n",
    "num_fit = np.polyval(fit, year)\n",
    "plt.plot(year, num, 'ro', label='原始数据')\n",
    "plt.plot(year, num_fit, 'b-',label='拟合曲线')\n",
    "year_later = np.arange(8, 11, 0.5)\n",
    "num_fit_curve = fit[0] * year_later + fit[1]#用一次函数拟合数据，fit[0]就是斜率，fit[1]就是常数项\n",
    "print(num_fit_curve)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "二次函数拟合的误差 [[ 2.51650344e-05 -2.01320282e-04  2.34873658e-04]\n",
      " [-2.01320282e-04  1.73974272e-03 -2.39571096e-03]\n",
      " [ 2.34873658e-04 -2.39571096e-03  5.12024340e-03]]\n",
      "一次函数拟合的误差 [[ 0.00014201 -0.00056806]\n",
      " [-0.00056806  0.003219  ]]\n",
      "[0.00653193 1.12458292 4.90655576]\n",
      "[1.17683833 4.84559111]\n"
     ]
    },
    {
     "data": {
      "text/plain": "[<matplotlib.lines.Line2D at 0x2179a8b70a0>]"
     },
     "execution_count": 280,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#8.6\n",
    "\n",
    "#先查看数据分布，再确定数据的拟合曲线\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import curve_fit\n",
    "year = np.arange(0, 9, 1)\n",
    "num = [5, 5.9945, 7.0932, 8.2744, 9.5073, 10.7555, 11.9804, 13.1465, 14.2247]\n",
    "plt.scatter(year,num)#看图像貌似是一条曲线，但是用一次函数，还是二次函数可以都尝试一下\n",
    "def func1(x, a, b, c):\n",
    "    return a*x**2 +b*x+c\n",
    "def func2(x,a,b):\n",
    "    return a*x+b\n",
    "popt1, pcov1 = curve_fit(func1, year, num) #拟合二次函数\n",
    "plt.plot(year, func1(year, *popt1), 'g--',\n",
    "              label='fit: a=%5.3f, b=%5.3f, c=%5.3f' % tuple(popt1))#可以看到二次函数拟合的效果还是不错的\n",
    "print('二次函数拟合的误差',pcov1)#二次函数误差貌似有点高\n",
    "popt2, pcov2 = curve_fit(func2, year, num)#拟合一次函数\n",
    "plt.plot(year, func2(year, *popt2), 'r-',\n",
    "              label='fit: a=%5.3f, b=%5.3f' % tuple(popt2))\n",
    "print('一次函数拟合的误差',pcov2)#一次函数的误差较小\n",
    "plt.legend(loc='best',fontsize = 12)\n",
    "print(popt1)\n",
    "print(popt2)\n",
    "year_later = np.arange(8, 11, 0.5)\n",
    "num_fit_curve1 = popt1[0] * year_later**2 + popt1[1]*year_later + popt1[2]#二次曲线预测\n",
    "num_fit_curve2 = popt2[0] * year_later + popt2[1]#一次曲线预测\n",
    "plt.plot(year_later,num_fit_curve1)\n",
    "plt.plot(year_later,num_fit_curve2)#从曲线分析，貌似一次曲线更符合需求"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 318,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[   60. -1800.     0.     0.]\n",
      " [   63. -2142.     0.     0.]\n",
      " [   64. -2432.     0.     0.]\n",
      " [   63. -2772.     0.     0.]\n",
      " [   61. -3050.     0.     0.]\n",
      " [   58. -3190.     0.     0.]\n",
      " [   53. -3074.     0.     0.]\n",
      " [   44. -2464.     0.     0.]\n",
      " [   39. -1833.     0.     0.]\n",
      " [   38. -1444.     0.     0.]\n",
      " [   41. -1230.     0.     0.]\n",
      " [   46. -1242.     0.     0.]]\n",
      "[[   0.    0.  -30. 1800.]\n",
      " [   0.    0.  -34. 2142.]\n",
      " [   0.    0.  -38. 2432.]\n",
      " [   0.    0.  -44. 2772.]\n",
      " [   0.    0.  -50. 3050.]\n",
      " [   0.    0.  -55. 3190.]\n",
      " [   0.    0.  -58. 3074.]\n",
      " [   0.    0.  -56. 2464.]\n",
      " [   0.    0.  -47. 1833.]\n",
      " [   0.    0.  -38. 1444.]\n",
      " [   0.    0.  -30. 1230.]\n",
      " [   0.    0.  -27. 1242.]]\n",
      "[[   60. -1800.     0.     0.]\n",
      " [   63. -2142.     0.     0.]\n",
      " [   64. -2432.     0.     0.]\n",
      " [   63. -2772.     0.     0.]\n",
      " [   61. -3050.     0.     0.]\n",
      " [   58. -3190.     0.     0.]\n",
      " [   53. -3074.     0.     0.]\n",
      " [   44. -2464.     0.     0.]\n",
      " [   39. -1833.     0.     0.]\n",
      " [   38. -1444.     0.     0.]\n",
      " [   41. -1230.     0.     0.]\n",
      " [   46. -1242.     0.     0.]\n",
      " [    0.     0.   -30.  1800.]\n",
      " [    0.     0.   -34.  2142.]\n",
      " [    0.     0.   -38.  2432.]\n",
      " [    0.     0.   -44.  2772.]\n",
      " [    0.     0.   -50.  3050.]\n",
      " [    0.     0.   -55.  3190.]\n",
      " [    0.     0.   -58.  3074.]\n",
      " [    0.     0.   -56.  2464.]\n",
      " [    0.     0.   -47.  1833.]\n",
      " [    0.     0.   -38.  1444.]\n",
      " [    0.     0.   -30.  1230.]\n",
      " [    0.     0.   -27.  1242.]]\n",
      "[ 3.   1.  -1.  -2.  -3.  -5.  -4.5 -2.5 -0.5  1.5  2.5  3.5  4.   4.\n",
      "  6.   6.   5.   3.  -1.  -4.5 -4.5 -4.  -1.5 -0.5]\n",
      "参数a,b,c,d为： [0.19074 0.00483 0.48289 0.00954]\n"
     ]
    }
   ],
   "source": [
    "#8.7\n",
    "\n",
    "#利用线性最小二乘方法，估算整体的最小值\n",
    "import numpy as np\n",
    "t0 = np.array([0,1,2,3,4,5,6,8,10,12,14,16,18])\n",
    "x0 = np.array([60,63,64,63,61,58,53,44,39,38,41,46,53])\n",
    "y0= np.array([30,34,38,44,50,55,58,56,47,38,30,27,26])\n",
    "dt = np.diff(t0)#输出t方向的离散差值\n",
    "dx = np.diff(x0)#输出x轴方向的离散差值\n",
    "dy = np.diff(y0)#输出y轴方向的离散差值\n",
    "temp = x0[:-1]*y0[:-1]#x与y的乘积\n",
    "mat1 = np.vstack([x0[:-1],-temp,np.zeros((2,12))]).T#按照列方向堆叠\n",
    "print(mat1)\n",
    "mat2 = np.vstack([np.zeros((2,12)),-y0[:-1],temp]).T#按照列方向堆叠\n",
    "print(mat2)\n",
    "mat = np.vstack([mat1,mat2])#构造线性方程组的系数矩阵\n",
    "print(mat)#堆叠形成左边的矩阵\n",
    "b = np.hstack([dx/dt,dy/dt])#按照行方向堆叠，构造线性方程组的常数项列\n",
    "print(b)\n",
    "cs = (np.linalg.pinv(mat))@b\n",
    "''''\n",
    "利用pinv函数求解mat的伪逆矩阵，\n",
    "奇异矩阵和非方阵没有逆矩阵，但是可以有伪逆矩阵\n",
    "Ax=b 如果A不是可逆举证，则x的最小化解为：A(L)*b\n",
    "'''\n",
    "print('参数a,b,c,d为：',np.round(cs,5))#给cs保留5位小数\n"
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